A majority of Australian Christians support same-sex marriage and think parliamentarians should vote on the issue as soon as possible.

A Galaxy Research poll of 1,000 Australian Christians has found 54% support marriage equality and 49% do not want the law to be changed to allow civil celebrants to refuse their services to same-sex couples based on conscientious objection.

It also found 61% do not like having conservative religious groups presenting their views on same-sex marriage as though they are speaking for all Christians in the country.

“I think it might even be sooner than everyone thinks, and your friends in Canberra are working on that outcome,” Pyne was recorded saying.

Two days after the tape was made public, it was revealed that federal Liberal senator Dean Smith and Liberal backbencher Trent Zimmerman had actually been working on a private members’ bill to legalise same-sex marriage through a conscience vote by MPs, rather than a non-binding plebiscite.

Their bill contradicted the Turnbull government’s official position, and Malcolm Turnbull quickly killed off the plan, saying legislation on same-sex marriage would not be brought to parliament “until there has been a vote of the Australian people”.

But the Galaxy poll has found 77% of Australian Christians believe all federal parliamentarians should be free to vote on same-sex marriage as soon as possible.

It found support for a free vote is strong across all Christian age groups, but strongest among millennials (aged 18-34) at 86%.

It also asked about civil celebrants’ right to refuse to marry same-sex couples.

At the moment, wedding service providers such as civil celebrants, or businesses such as florists or caterers, cannot legally refuse to provide their services to any couples seeking to marry.

But 49% of Australian Christians oppose a law change that would allow civil celebrants to refuse their services to same-sex couples on the ground of conscientious objection.

Only 31% supported a law change to allow refusal of civil celebrant services to same-sex couples, while 21% are undecided.

Shelley Argent, the national spokesperson for Parents and Friends of Lesbians and Gays, said with Australian Christians so conclusively behind marriage equality, it’s time for politicians “to have a free vote and get this done”.

“Changes to the Marriage Act have always been made through the parliamentary process and should remain so,” Argent said.

“Politicians should stop paying so much attention to conservative Christian advocacy organisations which a majority of Christians feel don’t represent them.”

“As a mother I want my gay son to have the same rights and responsibilities as his brother. One of the rights being the right to legally marry his partner and have it recognised in his home country,” she said.

The Very Reverend Peter Catt, the Dean of St John’s Cathedral and spokesperson for Progressive Christian Voice, said the poll proved that Australian Christians believe everyone should be treated equally and fairly without discrimination.

“I’m pleased to see Australian Christians holding firm to Christ’s injunction to treat others as we would like to be treated ourselves,” Catt said.

“I’m particularly pleased that most Christians feel their views on marriage equality are not represented by conservative religious groups. This means it’s time our leaders listened to a greater diversity of Christian voices.”